On least eigenvalues and least eigenvectors of real symmetric matrices and graphs

DOI10.1016/j.laa.2012.09.035zbMath1258.05078OpenAlexW2037317045MaRDI QIDQ1938694

Bo Zhou, Rundan Xing

Publication date: 22 February 2013

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.09.035

zbMATH Keywords

symmetric matrixleast eigenvalueleast eigenvectoradjacency matrix of graphs

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (3)

Estimating distance between an eigenvalue of a signed graph and the spectrum of an induced subgraph ⋮ On a conjecture for the signless Laplacian spectral radius of cacti with given matching number ⋮ The evolution of compact binary star systems

Cites Work

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• Bounds for the spectral radius of a graph when nodes are removed
• The least eigenvalue of the complements of trees
• A sharp upper bound on the maximal entry in the principal eigenvector of symmetric nonnegative matrix
• Graphs for which the least eigenvalue is minimal. I
• On maximal entries in the principal eigenvector of graphs
• A necessary and sufficient eigenvector condition for a connected graph to be bipartite
• On the bounds of maximal entries in the principal eigenvector of symmetric nonnegative matrix

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